A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed consists of preconditioner that increases the norm skew-symmetric part relative to rest and makes main diagonal coefficient matrix as close identity possible so preconditioned system is shifted possible. then solved via particular Minimal Residual Method Shifted Skew-Symmetric Systems (MRS). This leads (inner outer) where MRS has short-term recurrences satisfies an optimality condition. A inner designed skew-symmetry-preserving deflation strategy based on skew-Lanczos process. demonstrate robustness matrices from various applications.